Solve x2 – 3x = –8 using the quadratic formula.
Answers
Here is the step by step answer. hope it helps!
The solution to the quadratic equation x² - 3x + 8 = 0 is given by
x = ( 3/2 ) ± i ( √23/2 )
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
x² - 3x = -8
Adding 8 on both sides of the equation , we get
x² - 3x + 8 = 0 be equation (1)
Now , on simplifying the equation , we get
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
Substituting the values in the equation , we get
x = [ - ( -3 ) ± √ ( -3 )² - ( 4 ) ( 1 ) ( 8 ) ] / 2
On simplifying the equation , we get
x = [ 3 ± √ ( 9 - 32 ) ] / 2
x = ( 3/2 ) ± √ ( -23 ) / 2
x = ( 3/2 ) ± i ( √23/2 )
where i² = -1
Therefore , the value of x is x = ( 3/2 ) + i ( √23/2 ) , x = ( 3/2 ) - i ( √23/2 )
Hence , the solution to the equation is x = ( 3/2 ) ± i ( √23/2 )
To learn more about quadratic equations click :
https://brainly.com/question/25652857
#SPJ2
Related Questions
Share £1200 in the ratio 3:5.
Answers
so you have the amount.
amount: 1200
then you have the ratio
ratio: 3:5
you have the count.
count: 2
and then you have the shares
shares: 8
and the amount per share is 150.00
so the total amount of shares is the sum of each person's ratio so,
so 1:5:2:3:9 = 1 + 5 + 2 + 3 +9 = 20 shares. hope that helps you..
What is the solution to the following system of equations?
|3x - 2y = 12
[6x - 4y= 24
It has infinitely many solutions.
It has no solution.
It has one solution (2, -3).
It has one solution (4,0)
Answers
Explanation:
3x - 2y = 12
-2y = -3x + 12
y = -3/-2x + 12
y = 3/2x + 12
6x - 4y = 24
3x - 2y = 12 (divide both sides by 2)
y = 3/2x + 12
When 2 lines have the same slope and the same y intercept it means that the solution is infinitely many.
The cost price of a refridgator is $1850.00. A buyer who is given a discount of 5% for a cash purchase will pay
Answers
4x-2(4x-2) simplify in the lowest form
Answers
Answer:
-4x + 4
Step-by-step explanation:
4x - 2( 4x - 2 )
→ Expand out 2 ( 4x - 2 )
2 ( 4x - 2 ) = 8x - 4
→ Substitute the expanded bracket back into the expression
4x - (8x - 4)
→ Collect the 'x' values
-4x + 4
You are given the following information obtained from a random sample of 5 observations. 20 18 17 22 18 At 90% confidence, you want to determine whether or not the mean of the population from which this sample was taken is significantly less than 21. (Assume the population is normally distributed.) a) State the null and the alternative hypotheses. b) Compute the standard error of the mean. c) Determine the test statistic. d) Test to determine whether or not the mean of the population is significantly less than 21.
Answers
Answer:
a
The null hypothesis is
[tex]H_o : \mu = 21[/tex]
The Alternative hypothesis is
[tex]H_a : \mu< 21[/tex]
b
[tex]\sigma_{\= x} = 0.8944[/tex]
c
[tex]t = -2.236[/tex]
d
Yes the mean population is significantly less than 21.
Step-by-step explanation:
From the question we are given
a set of data
20 18 17 22 18
The confidence level is 90%
The sample size is n = 5
Generally the mean of the sample is mathematically evaluated as
[tex]\= x = \frac{20 + 18 + 17 + 22 + 18}{5}[/tex]
[tex]\= x = 19[/tex]
The standard deviation is evaluated as
[tex]\sigma = \sqrt{ \frac{\sum (x_i - \= x)^2}{n} }[/tex]
[tex]\sigma = \sqrt{ \frac{ ( 20- 19 )^2 + ( 18- 19 )^2 +( 17- 19 )^2 +( 22- 19 )^2 +( 18- 19 )^2 }{5} }[/tex]
[tex]\sigma = 2[/tex]
Now the confidence level is given as 90 % hence the level of significance can be evaluated as
[tex]\alpha = 100 - 90[/tex]
[tex]\alpha = 10[/tex]%
[tex]\alpha =0.10[/tex]
Now the null hypothesis is
[tex]H_o : \mu = 21[/tex]
the Alternative hypothesis is
[tex]H_a : \mu< 21[/tex]
The standard error of mean is mathematically evaluated as
[tex]\sigma_{\= x} = \frac{\sigma}{ \sqrt{n} }[/tex]
substituting values
[tex]\sigma_{\= x} = \frac{2}{ \sqrt{5 } }[/tex]
[tex]\sigma_{\= x} = 0.8944[/tex]
The test statistic is evaluated as
[tex]t = \frac{\= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 19 - 21 }{ 0.8944 }[/tex]
[tex]t = -2.236[/tex]
The critical value of the level of significance is obtained from the critical value table for z values as
[tex]z_{0.10} = 1.28[/tex]
Looking at the obtained value we see that [tex]z_{0.10}[/tex] is greater than the test statistics value so the null hypothesis is rejected
Please help me identify the rays!!!!
Answers
Answer:
D (The last choice)
Step-by-step explanation:
We know that rays are lines with a dot on one side and an arrow on the other. WE also know that lines have two arrows on each end. Keeping this in mind, we can identify which line segments and rays and lines.
A private jet can fly 1,095 miles in 3 hours with a tailwind but only 987 miles in 3 hours into a headwind find the speed of the jet in still air
Answers
Answer:
The speed of the jet is 347 mph and the speed of the wind is 18 mph.
Step-by-step explanation:
We have the following:
x = the speed of the jet in still air.
y = the speed of the wind
we know that the speed is equal to:
v = d / t
therefore the distance would be:
d = v * t
if we replace with the information of the exercise we have:
3 * (x + y) = 1095
3 * (x - y) = 987
we must solve this system of equations, add both equations and we are left:
3 * x + 3 * y = 1095
3 * x - 3 * y = 987
3 * x + 3 * y + 3 * x - 3 * y = 1095 + 987
6 * x = 2082
x = 2082/6 = 347
now to calculate y, we replace:
3 * (347 + y) = 1095
1041 + 3 * y = 1095
3 * y = 1095 - 1041
y = 54/3 = 18
The speed of the jet is 347 mph and the speed of the wind is 18 mph.
A square mesaures 80 yd on a side. Bob and Rob begin running from the same corner. Bob runs along a side to an adjacent corner, and Rob runs along a diagonal to an opposite corner. They arrive at their respective corners at the same time. If Bob's speed was 8mi/h, what was Rob's speed? Express your answer as a decimal to the nearest tenth.
Answers
Answer:
c = 11.3 mi/h
Step-by-step explanation:
Since Square has all of the same sides, hence bobs speed will be the same for all of the sides.
All of the sides are equal in a square
=> Let's consider the two sides along with the diagonal a right angled triangle
=> [tex]c^2 = a^2 + b^2[/tex]
Where c is the speed of Rob along the diagonal and b and c is the speed of Bob along the side
=> [tex]c^2 = 8^2+8^2[/tex]
=> [tex]c^2 = 64+64[/tex]
=> [tex]c^2 = 128\\[/tex]
Taking sq root on both sides
=> c = 11.3 mi/h
please help ASAP!!!!!!!!!
Answers
Answer:
sec B = 17 / 15
Step-by-step explanation:
Sec theta = hyp / adj
sec B = 17 / 15
Answer:
17/15
Step-by-step explanation:
The secant of an angle is the ratio of the hypotenuse to the adjacent angle (it is also the reciprocal of cosine).
secθ=hypotenuse/adjacent
sec(∠B)= hypotenuse/adjacent
The hypotenuse in this triangle is 17, because it is opposite the right angle or the little square.
sec(∠B)=17/adjacent
The side adjacent, or next to angle B is 15.
sec(∠B)= 17/15
This fraction cannot be reduced further, therefore the secant of angle B is 17/15.
F(x)=8*(1/2)^x table
Answers
Answer:
Show the table or make ur question a little more clear so I can help
Step-by-step explanation:
g Refer to these data for the next set of questions: The JMP output is below. Use it to answer the following questions. Write the estimated regression equation. Test for a significant linear regression at the α = 0.05 level of significance At x=, find the 95% confidence interval for μY|x, and verbally explain the answer. At x = 12, compute a 95% CI for μY|x, and verbally explain the answer. How do you explain the different widths of the intervals in parts (c) and (d)?
Answers
Use the Quadratic Formula to solve the equation ? x^2-2x=-9
Answers
Answer:
x=(2+ √-32)/2 or x=(2- √-32)/2
Step-by-step explanation:
x^2 - 2x = -9
x^2 - 2x + 9 =0
x = 2± (√(-2)^2 - 4*1*9)/2*1
Use the quadratic formula in the expression using a=1, b= -2, c=9
x = 2±√4-36 /2
x = 2+√4-36 or x = 2 - √4 - 32 /2
x = (2+√-32) /2 or x=( 2 - √-32 )/2
The solution for the given quadratic equation are (2+i5.7)/2 or (2-i5.7)/2.
The given quadratic equation is x²-2x=-9.
What is the quadratic formula?Quadratic formula is the simplest way to find the roots of a quadratic equation.
The roots of a quadratic equation ax² + bx + c = 0 are given by x = [-b ± √(b² - 4ac)]/2a.
By comparing x²-2x+9=0 with ax² + bx + c = 0, we get a=1, b=-2 and c=9
Substitute a=1, b=-2 and c=9 in the quadratic formula, we get
x = [2±√(-2)²-4×1×9)]/2×1
= [2±√4-36]/2
= (2±i5.7)/2
x = (2+i5.7)/2 or (2-i5.7)/2
Therefore, the solution for the given quadratic equation are (2+i5.7)/2 or (2-i5.7)/2.
To learn more about the quadratic formula visit:
https://brainly.com/question/11540485.
#SPJ5
The average student loan debt for college graduates is $25,800. Suppose that that distribution is normal and that the standard deviation is $14,150. Let X = the student loan debt of a randomly selected college graduate. Round all probabilities to 4 decimal places and all dollar answers to the nearest dollar The middle 20% of college graduates' loan debt lies between what two numbers?
Answers
Students in management science class have just received their grades on the first test. The instructor has provided information about the first test grades in some previous classes as well as the final average for the same students. Some of these grades have been sampled and are as follow:
1st test Grade 98 77 88 80 96 61 64 95 79
Final average 93 78 84 75 84 64 66 95 86
Develop a regression model that could be used to predict the final average in the course based on the first test grade.
Predict the final average of a students who made an 83 on the first test.
Give the value of r and r2 for this model.
Interpret the value of r2 in the context of this problem.
Answers
Answer:
The regression model is:
y = 20.29 + 0.73·x
Step-by-step explanation:
In this case a regression model is to be formed to predict the final average in the course based on the first test grade.
Use Excel to form the regression model.
The output is attached below.
The regression model is:
y = 20.29 + 0.73·x
Predict the final average of a students who made an 83 on the first test as follows:
y = 20.29 + 0.73·x
= 20.29 + 0.73 × 83
= 80.88
The final average of a students who made an 83 on the first test would be 80.88.
From the output:
R² = 0.839
Then the correlation coefficient will be:
[tex]r=\sqrt{R^{2}}=\sqrt{0.839}=0.91597\approx 0.92[/tex]
The value of r is 0.92.
The coefficient of determination R² specifies the percentage of the variance in the dependent-variable (Y) that is forecasted or explained by linear regression and the forecaster variable (X, also recognized as the independent-variable).
In this case, the R² value of 0.839 implies that 83.9% of the variation in the final average can be explained by the grades in the first test.
A subscription for 15 magazines cost $45. the same company is offereing 25 magazines for $70. which is a better deal? why?
Answers
Answer:
25 magazines for $70. (For why, read explanation)
Step-by-step explanation:
We can find the unit price of each of these deals by dividing the cost and the quantity.
[tex]\frac{45}{15}[/tex] = 3, so the first deal is $3 per magazine.
[tex]\frac{70}{25}[/tex] = 2.8, so the second deal is $2.80 per magazine.
Therefore, 25 magazines for $70 is a better deal.
Hope this helped!
What is the solution for x in the given equation? (root)9x+7+ (root)2x=7 A. x = 18 and x = 2 B. x = 18 C. x = 2 D. x = 18 and x = -2
Answers
Answer:
C. x = 2
Step-by-step explanation:
[tex] \sqrt{9x + 7} + \sqrt{2x} = 7 [/tex]
Since you have square roots, you need to separate the square roots and square both sides.
[tex] \sqrt{9x + 7} = 7 - \sqrt{2x} [/tex]
Now that one square root is on each side of the equal sign, we square both sides.
[tex] (\sqrt{9x + 7})^2 = (7 - \sqrt{2x})^2 [/tex]
[tex] 9x + 7 = 49 - 14\sqrt{2x} + 2x [/tex]
Now we isolate the square root and square both sides again.
[tex] 7x - 42 = -14\sqrt{2x} [/tex]
Every coefficient is a multiple of 7, so to work with smaller numbers, we divide both sides by 7.
[tex] x - 6 = -2\sqrt{2x} [/tex]
Square both sides.
[tex] (x - 6)^2 = (-2\sqrt{2x})^2 [/tex]
[tex] x^2 - 12x + 36 = 4(2x) [/tex]
[tex] x^2 - 20x + 36 = 0 [/tex]
We need to try to factor the left side.
-2 * (-18) = 36 & -2 + (-18) = -20, so we use -2 and -18.
[tex] (x - 2)(x - 18) = 0 [/tex]
[tex] x = 2 [/tex] or [tex] x = 18 [/tex]
Since solving this equation involved the method of squaring both sides, we much check for extraneous solutions by testing our two solutions in the original equation.
Test x = 2:
[tex] \sqrt{9x + 7} + \sqrt{2x} = 7 [/tex]
[tex] \sqrt{9(2) + 7} + \sqrt{2(2)} = 7 [/tex]
[tex] \sqrt{25} + \sqrt{4} = 7 [/tex]
[tex] 5 + 2 = 7 [/tex]
[tex] 5 = 5 [/tex]
We have a true equation, so x = 2 is a true solution of the original equation.
Now we test x = 18.
[tex] \sqrt{9x + 7} + \sqrt{2x} = 7 [/tex]
[tex] \sqrt{9(18) + 7} + \sqrt{2(18)} = 7 [/tex]
[tex] \sqrt{162 + 7} + \sqrt{36} = 7 [/tex]
[tex] \sqrt{169} + 6 = 7 [/tex]
[tex] 13 + 6 = 7 [/tex]
[tex] 19 = 7 [/tex]
Since 19 = 7 is a false equation, x = 18 is not a true solution of the original equation and is discarded as an extraneous solution.
Answer: C. x = 2
Evaluate the expression when a=4 and y=-6.
-a+3y
a.
hi
Answers
Answer:
- 22Step-by-step explanation:
Given,
a = 4
y = -6
Now,
[tex] - a + 3y[/tex]
Plug the values
[tex] = - 4 + 3 \times ( - 6)[/tex]
Multiply the numbers
[tex] = - 4 + ( - 18)[/tex]
When there is a (+) in front of an expression in parentheses, the expression remains the same.
[tex] = - 4 - 18[/tex]
Calculate
[tex] = - 22[/tex]
Hope this helps..
Best regards!!
Answer:
14
Step-by-step explanation:
-4 + 3(6)
-4+18
14
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Consider the functions given below. SEE FILE ATTATCHED
Answers
Answer:
1. [tex] P(x) [/tex] ÷ [tex] Q(x) [/tex]---> [tex] \frac{-3x + 2}{3(3x - 1)} [/tex]
2. [tex] P(x) + Q(x) [/tex]---> [tex]\frac{2(6x - 1)}{(3x - 1)(-3x + 2)}[/tex]
3. [tex] P(x) - Q(x) [/tex]---> [tex] \frac{-2(12x - 5)}{(3x - 1)(-3x + 2)} [/tex]
4. [tex] P(x)*Q(x) [/tex] --> [tex] \frac{12}{(3x - 1)(-3x + 2)} [/tex]
Step-by-step explanation:
Given that:
1. [tex] P(x) = \frac{2}{3x - 1} [/tex]
[tex] Q(x) = \frac{6}{-3x + 2} [/tex]
Thus,
[tex] P(x) [/tex] ÷ [tex] Q(x) [/tex] = [tex] \frac{2}{3x - 1} [/tex] ÷ [tex] \frac{6}{-3x + 2} [/tex]
Flip the 2nd function, Q(x), upside down to change the process to multiplication.
[tex] \frac{2}{3x - 1}*\frac{-3x + 2}{6} [/tex]
[tex] \frac{2(-3x + 2)}{6(3x - 1)} [/tex]
[tex] = \frac{-3x + 2}{3(3x - 1)} [/tex]
2. [tex] P(x) + Q(x) [/tex] = [tex] \frac{2}{3x - 1} + \frac{6}{-3x + 2} [/tex]
Make both expressions as a single fraction by finding, the common denominator, divide the common denominator by each denominator, and then multiply by the numerator. You'd have the following below:
[tex] \frac{2(-3x + 2) + 6(3x - 1)}{(3x - 1)(-3x + 2)} [/tex]
[tex] \frac{-6x + 4 + 18x - 6}{(3x - 1)(-3x + 2)} [/tex]
[tex] \frac{-6x + 18x + 4 - 6}{(3x - 1)(-3x + 2)} [/tex]
[tex] \frac{12x - 2}{(3x - 1)(-3x + 2)} [/tex]
[tex] = \frac{2(6x - 1}{(3x - 1)(-3x + 2)} [/tex]
3. [tex] P(x) - Q(x) [/tex] = [tex] \frac{2}{3x - 1} - \frac{6}{-3x + 2} [/tex]
[tex] \frac{2(-3x + 2) - 6(3x - 1)}{(3x - 1)(-3x + 2)} [/tex]
[tex] \frac{-6x + 4 - 18x + 6}{(3x - 1)(-3x + 2)} [/tex]
[tex] \frac{-6x - 18x + 4 + 6}{(3x - 1)(-3x + 2)} [/tex]
[tex] \frac{-24x + 10}{(3x - 1)(-3x + 2)} [/tex]
[tex] = \frac{-2(12x - 5}{(3x - 1)(-3x + 2)} [/tex]
4. [tex] P(x)*Q(x) = \frac{2}{3x - 1}* \frac{6}{-3x + 2} [/tex]
[tex] P(x)*Q(x) = \frac{2*6}{(3x - 1)(-3x + 2)} [/tex]
[tex] P(x)*Q(x) = \frac{12}{(3x - 1)(-3x + 2)} [/tex]
Composite functions involve combining multiple functions to form a new function
The functions are given as:
[tex]P(x) = \frac{2}{3x - 1}[/tex]
[tex]Q(x) = \frac{6}{-3x + 2}[/tex]
[tex]P(x) \div Q(x)[/tex] is calculated as follows:
[tex]P(x) \div Q(x) = \frac{2}{3x - 1} \div \frac{6}{-3x + 2}[/tex]
Express as a product
[tex]P(x) \div Q(x) = \frac{2}{3x - 1} \times \frac{-3x + 2}{6}[/tex]
Divide 2 by 6
[tex]P(x) \div Q(x) = \frac{1}{3x - 1} \times \frac{-3x + 2}{3}[/tex]
Multiply
[tex]P(x) \div Q(x) = \frac{-3x + 2}{3(3x - 1)}[/tex]
Hence, the value of [tex]P(x) \div Q(x)[/tex] is [tex]\frac{-3x + 2}{3(3x - 1)}[/tex]
P(x) + Q(x) is calculated as follows:
[tex]P(x) + Q(x) = \frac{2}{3x - 1} + \frac{6}{-3x + 2}[/tex]
Take LCM
[tex]P(x) + Q(x) = \frac{2(-3x + 2) + 6(3x - 1)}{(3x - 1)(-3x + 2)}[/tex]
Open brackets
[tex]P(x) + Q(x) = \frac{-6x + 4 + 18x - 6}{(3x - 1)(-3x + 2)}[/tex]
Collect like terms
[tex]P(x) + Q(x) = \frac{18x-6x + 4 - 6}{(3x - 1)(-3x + 2)}[/tex]
[tex]P(x) + Q(x) = \frac{12x - 2}{(3x - 1)(-3x + 2)}[/tex]
Factor out 2
[tex]P(x) + Q(x) = \frac{2(6x -1)}{(3x - 1)(-3x + 2)}[/tex]
Hence, the value of P(x) + Q(x) is [tex]\frac{2(6x -1)}{(3x - 1)(-3x + 2)}[/tex]
P(x) - Q(x) is calculated as follows:
[tex]P(x) - Q(x) = \frac{2}{3x - 1} - \frac{6}{-3x + 2}[/tex]
Take LCM
[tex]P(x) - Q(x) = \frac{2(-3x + 2) - 6(3x - 1)}{(3x - 1)(-3x + 2)}[/tex]
Open brackets
[tex]P(x) - Q(x) = \frac{-6x + 4 - 18x +6}{(3x - 1)(-3x + 2)}[/tex]
Collect like terms
[tex]P(x) - Q(x) = \frac{-18x-6x + 4 + 6}{(3x - 1)(-3x + 2)}[/tex]
[tex]P(x) - Q(x) = \frac{-24x +10}{(3x - 1)(-3x + 2)}[/tex]
Factor out -2
[tex]P(x) - Q(x) = \frac{-2(12x -5)}{(3x - 1)(-3x + 2)}[/tex]
Hence, the value of P(x) - Q(x) is [tex]\frac{-2(12x -5)}{(3x - 1)(-3x + 2)}[/tex]
P(x) * Q(x) is calculated as follows:
[tex]P(x) \times Q(x) = \frac{2}{3x - 1} \times \frac{6}{-3x + 2}[/tex]
Multiply
[tex]P(x) \times Q(x) = \frac{12}{(3x - 1)(-3x + 2)}[/tex]
Hence, the value of P(x) * Q(x) is [tex]\frac{12}{(3x - 1)(-3x + 2)}[/tex]
Read more about composite functions at:
https://brainly.com/question/10687170
What is the slope of the line that contains the points (2,5) and (4, - 3)?
Answers
Answer:
-4
Step-by-step explanation:
The slope would be (5 - (-3)) / (2 - 4) = 8 / -2 = -4.
Answer:
[tex]\huge\boxed{\text{The slope}\ m=-4}[/tex]
Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
(x₁; y₁), (x₂; y₂) - points on a line
We have the points:
[tex](2;\ 5)\to x_1=2;\ y_1=5\\(4;\ -3)\to x_2=4;\ y_2=-3[/tex]
Substitute:
[tex]m=\dfrac{-3-5}{4-2}=\dfrac{-8}{2}=-4[/tex]
Explain how using dot paper helps in drawing perspective drawings.
Answers
Answer:
Dot paper helps to understand and bring in the big picture in perspective drawing.
Step-by-step explanation:
Dot paper helps to understand patterns and features of the big picture. It helps to understand patterns at various intervals. Drawing with perspective helps to understand the big idea. Perspective reveals your point of view and helps gravitate your idea of the spatial onto paper. You can express linear perspectives.
You can use your principles of perspective drawing to create a perception of your world and your world view through your art.
need help thankssssss
Answers
Answer:
301.44
Step-by-step explanation:
V=π r² h
V=π (4)² (12)
V= 603.19
divide by 2 to find half full: ≈ 301
301.44
6( 5/12a− 5/18 )− 5/8 (4a+ 2/5 ) simplify
Answers
Answer:
think its 3a 3.83838
Step-by-step explanation:
Answer:
-23/11
Step-by-step explanation:
x² + 2x-3
f(x) =
x2 + 5x + 6
(a) What is the domain of the function? (Write your answer in interval notation.)
(b) Determine the equation of the vertical asymptotes of f. If there are none, write, 'None!
(C) Determine the equation of the horizontal asymptote of f. If there is none, write, 'None'.
(d) Find the y-intercept(s).
(e) Find the x-intercept(s).
Click to select your answer(s).
Answers
Answer:
x4+7x+3
Step-by-step explanation:
What is the exact volume of the cylinder? Enter your answer, in terms of π, in the box. m³ $\text{Basic}$ $x$$y$$x^2$$\sqrt{ }$$\frac{x}{ }$ $x\frac{ }{ }$ $x^{ }$$x_{ }$$\degree$$\left(\right)$$\abs{ }$$\pi$$\infty$ A cylinder that is 2.5 m tall with a radius of 1.5 m
Answers
Answer:
[tex]5.625\pi[/tex] m³.
Step-by-step explanation:
The volume of a cylinder is found by calculating pi * r^2 * h.
In this case, h = 2.5, and r = 1.5.
pi * 1.5^2 * 2.5
= pi * 2.25 * 2.5
= pi * 5.625
So, the exact volume of the cylinder is [tex]5.625\pi[/tex] m³.
Hope this helps!
Answer: Volume of Cylinder: [tex]\pi r^{2} *h[/tex]
5.625π m.
Step-by-step explanation:
[tex]\pi r^{2} *h[/tex] Cylinder Area Formula
[tex]\pi *1.5^{2} *2.5[/tex] Substitution
[tex]\pi * 2.25 *2.5[/tex] Exponent
[tex]\pi *5.625[/tex] Multiply
[tex]5.625\pi[/tex] Answer
A circle is centered at CC-1, -3) and has a radius of 6.
Where does the point P(-6, -6) lie?
Choose 1 answer:
Inside the circle
On the circle
Outside the circle
Answers
Answer:
outside the circle i think
Step-by-step explanation:
Answer:
inside the circle
Step-by-step explanation:
I need help with this problem.
Answers
________________________Alike______________________
→ Both of the lines are proportional meaning they go through the origin.
→ Both of the lines have a positive slope meaning the slope goes towards the top right corner.
__________________________________________________
_____________________Difference_____________________
→ The 2 lines have different slopes, the first one has a slope of 1/3x whereas the 2nd one has a slope of 3x.
→ The points that create the lines are totally different, no two points are the same.
__________________________________________________
Which is the simplified form of the expression 3(7/5x + 4) - 2(3/2 - 5/4x)?
1) -39/5x - 11/2
2)67/10x + 9
3) 3/10x + 5/2
4) 15 + 76/10x
Answers
Answer:
(67/10)x + 9 (answer [2])
Step-by-step explanation:
3(7/5x + 4) - 2(3/2 - 5/4x). after the indicated multiplication has been carried out, is:
(21/5)x + 12 - 3 + (5/2)x
Combining like terms, we get (4.2 + 2.5)x + 9, or
6.7x + 9, or (67/10)x + 9 (answer [2])
A restaurant operator in Accra has found out that during the partial lockdown, if she sells a plate of her food for GH¢20 each, she can sell 300 plates, but for each GH¢5 she raises the price, 10 less plates are sold.
Draw a table of cost relating to number of plates using 6 values of cost and its corresponding number of plates bought.
What price in GH¢ should she sell the plates to maximize her revenue?
Answers
Answer:
Step-by-step explanation:
First, note this parameters from the question.
We let x = number of $5 increases and number of 10 decreases in plates sold.
Our Revenue equation is:
R(x) = (300-10x)(10+5x)
We expand the above equation into a quadratic equation by multiplying each bracket:
R(x) = 3000 + 1500x - 3000x - 1500x^2
R(x) = -1500x^2 - 1500x + 3000 (collect like terms)
Next we simplify, by dividing through by -1500
= 1500x^2/1500 - 1500x/1500 + 3000/1500
= X^2 - x + 2
X^2 - x + 2 = 0
Next, we find the axis of symmetry using the formula x = -b/(2*a) where b = 1, a = 1
X = - (-1)/2*1
X = 1/2
Number of $5 increases = $5x1/2 = $2.5
=$2.5 + $20 = $22.5 ticket price gives max revenue.
In the following problem, the expression is the right side of the formula for cos (alpha - beta) with particular values for alpha and beta. cos (79 degree) cos (19 degree) + sin (79 degree) sin (19 degree)
Identify alpha and beta in each expression.
The value for alpha: degree
The value for beta: degree
Write the expression as the cosine of an angle. cos degree
Find the exact value of the expression. (Type an exact answer, using fraction, radicals and a rationalized denominator.)
Answers
Answer:
1. [tex]\alpha = 79[/tex] and [tex]\beta = 19[/tex]
2. [tex]cos(60)[/tex]
3. [tex]cos(60) = \frac{1}{2}[/tex]
Step-by-step explanation:
Given
[tex]cos(\alpha - \beta )[/tex]
[tex]cos(79)cos(19) + sin(79)sin(19)[/tex]
Solving for [tex]\alpha[/tex] and [tex]\beta[/tex]
In trigonometry;
[tex]cos(\alpha - \beta ) = cos\alpha\ cos\beta + sin\alpha\ sin\beta[/tex]
Equate the above expression to [tex]cos(79)cos(19) + sin(79)sin(19)[/tex]
[tex]cos(\alpha - \beta ) = cos\alpha\ cos\beta + sin\alpha\ sin\beta[/tex] and [tex]cos(\alpha - \beta ) = cos(79)cos(19) + sin(79)sin(19)[/tex]
By comparison
[tex]cos\alpha\ cos\beta + sin\alpha\ sin\beta = cos(79)cos(19) + sin(79)sin(19)[/tex]
Compare expression on the right hand side to the left hand side
[tex]cos\alpha\ cos\beta = cos(79)cos(19) \\\\ sin\alpha\ sin\beta = sin(79)sin(19)[/tex]
This implies that
[tex]cos\alpha\ = cos(79)\\cos\beta = cos(19) \\\\ and\\\\sin\alpha\ = sin(79)\\sin\beta = sin(19)[/tex]
By further comparison
[tex]\alpha = 79[/tex] and [tex]\beta = 19[/tex]
Substitute [tex]\alpha = 79[/tex] and [tex]\beta = 19[/tex] in [tex]cos(\alpha - \beta )[/tex]
[tex]cos(\alpha - \beta ) = cos(79 - 19)[/tex]
[tex]cos(\alpha - \beta ) = cos(60)[/tex]
Hence, the expression is [tex]cos(60)[/tex]
Solving for the exact values;
Express [tex]cos(60)[/tex] as a difference of angles
[tex]cos(60) = cos(90 - 30)[/tex]
Recall that [tex]cos(\alpha - \beta ) = cos\alpha\ cos\beta + sin\alpha\ sin\beta[/tex]
So;
[tex]cos(90- 30 ) = cos(90) cos(30) + sin(90) sin(30)[/tex]
------------------------------------------------------------------------------------
In trigonometry;
[tex]cos(90) = 0[/tex]; [tex]cos(30) = \frac{\sqrt{3}}{{2}}[/tex]; [tex]sin(90) = 1[/tex]; [tex]sin(30) = \frac{1}{2}[/tex];
---------------------------------------------------------------------------
[tex]cos(90- 30 ) = cos(90) cos(30) + sin(90) sin(30)[/tex] becomes
[tex]cos(90- 30 ) = 0 * \frac{\sqrt{3}}{2} + 1 * \frac{1}{2}[/tex]
[tex]cos(90- 30 ) = 0 + \frac{1}{2}[/tex]
[tex]cos(90- 30 ) = \frac{1}{2}[/tex]
Hence;
[tex]cos(60) = \frac{1}{2}[/tex]
Jose added up his work hours for his paycheck. Last week he worked hours 25 5/8. This week he worked hours 32 5/6. How many total hours did he work in two weeks? with steps
Answers
Answer:
58 hours
Step-by-step explanation:
First week: 25 5/8 hours = 25 hrs 37 mins and 30 sec
Second weeK: 32 5/6 hrs = 32 hrs and 50 mins
To find the toal time in minutes
(37 + 50) mins = 1 hr 27 mins
Threfore, total number of hours he worked in two weeks:
(25 + 32 + 1) hrs = 58 hours